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Simplifying 3x2 + 21x + -5 = 0 Reorder the terms: -5 + 21x + 3x2 = 0 Solving -5 + 21x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 7x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 7x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 7x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 7x + x2 = 0 + 1.666666667 7x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 7x + x2 = 1.666666667 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 1.666666667 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 1.666666667 + 12.25 Combine like terms: 1.666666667 + 12.25 = 13.916666667 12.25 + 7x + x2 = 13.916666667 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 13.916666667 Calculate the square root of the right side: 3.730504881 Break this problem into two subproblems by setting (x + 3.5) equal to 3.730504881 and -3.730504881.Subproblem 1
x + 3.5 = 3.730504881 Simplifying x + 3.5 = 3.730504881 Reorder the terms: 3.5 + x = 3.730504881 Solving 3.5 + x = 3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.730504881 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.730504881 + -3.5 x = 3.730504881 + -3.5 Combine like terms: 3.730504881 + -3.5 = 0.230504881 x = 0.230504881 Simplifying x = 0.230504881Subproblem 2
x + 3.5 = -3.730504881 Simplifying x + 3.5 = -3.730504881 Reorder the terms: 3.5 + x = -3.730504881 Solving 3.5 + x = -3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.730504881 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.730504881 + -3.5 x = -3.730504881 + -3.5 Combine like terms: -3.730504881 + -3.5 = -7.230504881 x = -7.230504881 Simplifying x = -7.230504881Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.230504881, -7.230504881}
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